- Recently an explicit resolution of the Calabi-Yau cone over the inhomogeneous five-dimensional Einstein-Sasaki space Y2, 1 was obtained. It was constructed by specialising the parameters in the BPS limit of recently-discovered Kerr-NUT-AdS metrics in higher dimensions. We study the occurrence of such non-singular resolutions of Calabi-Yau cones in a more general context. Although no further six-dimensional examples arise as resolutions of cones over the Lp q r Einstein-Sasaki spaces, we find general classes of non-singular cohomogeneity-2 resolutions of higher-dimensional Einstein-Sasaki spaces. The topologies of the resolved spaces are of the form of an R2 bundle over a base manifold that is itself an S2 bundle over an Einstein-Khler manifold.